Just wanted to offer you a few articles and troubleshooting tips that I have been using for Time Machine backup issues.
Both of these articles are an excellent source of information to really give you an idea of what goes on "behind the scenes" during the TM backup process:
Although the second article refers to macOS Catalina, it is still valid with macOS Monterey.
FWIW, I have found the Mints app invaluable in troubleshooting TM. I used to do this via commands in Terminal, but the app makes this far easier. Hopefully, it will shed some light on what's going on with TM on your Mac. Basically, I have found TM to have become less reliable since macOS Sierra. Initially, with just backups to the Time Capsule, but now with directly attached drives as well. So far, TM backups to my Synology NAS has been "rock solid." As such, although I continue to use TM, I rely on other backup tools (like Carbon Copy Cloner) in addition.